Cracking The SAT Premium

A   3-4-5   triangle    may be

hiding, disguised   as  6-8-10

or  18-24-30.   It’s    all the

same    ratio,  though, so  be

on  the lookout.

ETS also likes to use right triangles with sides that are simply multiples of the common Pythagorean
triplets. For example, you might see a 6-8-10 or a 10-24-26 triangle. These sides are simply the sides of
the 3-4-5 and 5-12-13 triangles multiplied by 2.

There are two types of special right triangles that have a specific ratio of angles. They are the
30°-60°-90° triangle and the 45°-45°-90° triangle. The sides of these triangles always have the same
fixed ratio to each other. The ratios are as follows:

Let’s talk about a 45°-45°-90° triangle first. Did you notice that this is also an isosceles right triangle?
The sides will always be the same. And the hypotenuse will always be the side times . Its ratio of side

to side to hypotenuse is always 1:1: . For example, if you have a 45°-45°-90° triangle with a side of 3,
then the second side will also be 3 and the hypotenuse will be 3.

Now let’s talk about a 30°-60°-90° triangle. The ratio of shorter side to longer side to hypotenuse is
always 1: :2. For example, if the shorter side of a 30°-60°-90° triangle is 5, then the longer side would
be 5 and the hypotenuse would be 10.

Symbols

Things  aren’t  always  written out on  the SAT.    Here’s  a   list    of  symbols you might   see,    along   with    a

translation of  each    one into    English:

Symbol Meaning

∆ABC triangle   ABC

AB line segment AB

AB the  length  of  line    segment AB